wind turbine propulsion of ships

8/12/2019 Wind Turbine Propulsion of Ships

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Second International Symposium on Marine Propulsorssmp11, Hamburg, Germany, June 2011

Wind Turbine Propulsion of Ships

Eirik Bckmann

1

, Sverre Steen

1

1Department of Marine Technology, Norwegian University of Science and Technology (NTNU), Trondheim, Norway

ABSTRACT

In this paper, the benefits and limitations of wind turbine

propulsion of ships are discussed. When designing the

wind turbine blades for a wind turbine-powered vessel, the

objective is not to maximize the power output, but to max-

imize the net forward force. The net forward force is the

forward force from the water propeller minus the back-ward force on the wind turbine. This objective results in

a different blade design than that of modern commercial

horizontal-axis wind turbines. A blade element theory ap-

proach to the design of optimal blades for wind turbine

powered boats and vehicles is used to design a wind tur-

bine for auxiliary propulsion of a 150 m long tanker. The

optimized blade design is shown to result in a higher fuel

saving for the ship, when sailing a given route at 10 knots,

than what is attained with a commercial wind turbine of the

same rotor diameter onboard the ship. Finally, the same

ship is equipped with wingsails instead of a wind turbinefor auxiliary propulsion, in order to compare the fuel sav-

ings. It is seen that the fuel saving is slightly higher when

employing the optimally designed wind turbine than when

employing wingsails of equivalent sail area as the wind tur-

bine rotor disk area.

Keywords

Wind turbine; wingsail; ship propulsion; blade element the-

ory; fuel saving.

1 INTRODUCTION

Increasing focus on reduction of CO2 emissions and thepossibility of future severe shortage of oil have spurred

renewed interest in wind as supplementary propulsion of

merchant ships. Several alternative solutions have been

considered, like kites, conventional soft sails, rigid sails,

Flettner rotors, and wind turbines. A tempting aspect of

wind turbine propulsion is that it can provide propulsive

force when sailing directly upwind, something that is im-

possible with the other mentioned forms of wind-assisted

propulsion.

In the last decades, vertically oriented airfoils, known as

wingsails, have at an increasing rate replaced soft sails asthey are aerodynamically more efficient when a high lift-

to-drag ratio is important. Indeed, the winner of the 33rd

Americas Cup (2010), BMW Oracle Racings trimaran,

USA-17, was fitted with a 68 m high rigid wingsail, replac-

ing the traditional soft main sail. Wingsails have also suc-

cessfully been fitted on several commercial ships for auxil-

iary propulsion. A recent summary of this is given byBose

(2008). Shukla and Ghosh (2009)estimated the fuel sav-

ing for a wingsail-equipped ship sailing Mumbai - Durban- Mumbai at 7 knots to be 8.3%. As far as the authors are

aware of, no merchant ships have yet been equipped with a

wind turbine for propulsive power generation. One reason

for this is that wind turbine propulsion generally provides

higher propulsive force than wingsails per turbine/sail area

only when the ship speed is less than about half the wind

speed (Blackford, 1985). This implies that for wind tur-

bine propulsion to be the preferred form of wind-assisted

ship propulsion, a ship cruising at 15 knots must sail an

extraordinary windy route with wind speeds above 15 m/s.

The other alternative is, of course, to reduce the ship speed,a measure which in itself will reduce fuel consumption.

The height, or air draft, is a limiting factor for both

wind turbine ships and ships equipped with soft or rigid

sails. The bridges that cross the seaward approaches to the

worlds major ports restrict the air draft of wind-assisted

ships to about 60 m, unless the wind turbine tower, wing-

sails or masts can be folded down. This means that for

a wind turbine-powered ship of length 150 m, the diame-

ter of a non-foldable horizontal-axis wind turbine on deck

is limited to about 40 m, considering the freeboard and a

safety clearance from the blade tips to the deck. When itcomes to stability issues, the increased heel angle due to

the wind turbine is shown in this paper to be negligible.

Fig. 1 shows the required propulsive power as a func-

tion of ship length for different scalings of a tanker hull

at 5, 7.5, 10, and 12.5 knots, as well as the power out-

put from Vestas wind turbines of varying diameters (The

Wind Power, 2010). Hull data for the full scale ship can

be found at http://www.gothenburg2010.org/

kvlcc2_gc.html. The residual resistance for the dif-

ferent ship lengths and speeds is found using Hollen-

bachs method (Hollenbach, 1998). The transverse pro-jected area above the waterline, AT S, is assumed to be

AT S= 1100m2

LWL [m]325.5

2, whereLW L is the length
http://www.gothenburg2010.org/kvlcc2_gc.htmlhttp://www.gothenburg2010.org/kvlcc2_gc.htmlhttp://www.gothenburg2010.org/kvlcc2_gc.htmlhttp://www.gothenburg2010.org/kvlcc2_gc.htmlhttp://www.gothenburg2010.org/kvlcc2_gc.html


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of waterline. The corresponding air drag coefficient with

respect toAT Sis assumed to beCDS= 0.8. The required

propulsive power is calculated as the total resistance times

the ship speed divided by a total efficiency factor of 0.7.

2 OPTIMAL WIND TURBINE DESIGN

2.1 Axial momentum theory

First, let us look at the simple axial momentum theory to

see how the task of designing an optimal wind turbine for

ship propulsion results in a different blade design than a

wind turbine designed to maximize the power output. Con-

sider a wind turbine-powered ship that is sailing at an angle

to the apparent wind, see Fig.2. The true wind direction

relative to the ship course is . The wind speed isW and

the ship speed isu, which together give the apparent wind

speedU. From axial momentum theory(Hansen, 2008),

the component of the force on the wind turbine parallel tothe ships course is given by

FW = 2aU2a(1 a)A cos , (1)

where a is the mass density of air, A is the turbine ro-

tor disk area, andais the axial induction factor. The power

generated by the wind turbine is from axial momentum the-

ory

P = 2aU3a(1 a)2A. (2)

The forward force from the water propeller is then

F = P u

, (3)

where is the overall propulsive efficiency, which accounts

for losses in the power transmission between the wind tur-

bine and the water propeller, as well as water propeller

losses. The net forward force,Fnet = F FW, then be-

comes

Fnet= P

u 2aU

2a(1 a)A cos . (4)

Inserting Eq. (2) into Eq. (4), and differentiating with re-

spect toagives

dFnetda

= 2aU2A

U

u (1 4a + 3a2) (1 2a)cos

. (5)

Setting Eq.(5) equal to zero to find a maximum value for

Fnet leads to a quadratic equation which has the solution

a=(2 cos 4)

6

(2 cos 4)2 12( cos )

6

, (6)

where = Uu . We see from Eq. (6) that if not ap-

proaches zero when u approaches zero, u will approach in-

finity, and we cannot use Eqs.(4), (5) or (6). If the ship is

sailing directly upwind at half the wind speed and = 0.7,

Eq. (6)givesa = 0.22, ora = 0.80. Momentum theory is

not valid fora >0.4(Hansen, 2008), so the valid solution

is a = 0.22. If we instead want to maximize the power

output from the wind turbine, we differentiate Eq.(2) with

respect to a, and set the resulting equation equal to zero.

We then find thata = 13

ora = 1. Calculating the power

coefficient defined as

CP = P1

2aU3A

= 4a(1 a)2 (7)

witha = 13

, we get CP = 16/27, which is known as the

Betz limit.

Inserting these two values ofa gives the results shown in

Table 1. We see that although the power from the wind

turbine that is optimized for ship propulsion is 10% less,

the backward force is 23% less, resulting in a net forward

force that is23% higher than that of the wind turbine that

is optimized for power, for the given values of,, and uU.

Table 1: Backward thrust, power and net forward force from

axial momentum theory.

a 0.22 1/3

FW/(aU2A) 0.3423 0.4444

P/(aU3A) 0.2673 0.2963

Fnet/(aU2A) 0.2190 0.1778

2.2 Blade element theory

Blackford(1985) showed how classical blade element the-

ory can be used to design optimal wind turbine blades for

a wind turbine-powered vessel. Blackfords approach is

briefly presented here with the original notation, and ap-

plied to design the wind turbine blades for a notional wind

turbine ship.

Ship course

WU

u

'

Figure 2: Sketch of wind and ship velocity vectors.

The apparent wind speed, with respect to the wind turbine-

powered vessel, see Fig.2, is given by

U =W(1 + f2 + 2fcos )1/2, (8)

wheref=u/Wis the ship speed to wind speed ratio. The

angle, which is the angle between the apparent wind and


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Wind turbine power vs diameter, regression line

Wind turbine power vs diameter

Propulsive power at 12.5 kn vs ship length

Propulsive power at 10 kn vs ship length

Propulsive power at 7.5 kn vs ship length

Propulsive power at 5 kn vs ship length

Power[kW]

Wind turbine diameter [m] or ship length 14

[m]

0 10 20 30 40 50 60 70 80 90 100

0

2000

4000

6000

8000

Figure 1: Wind turbine diameter vs power output for Vestas wind turbines, and ship length vs required propulsive power for

scalings of a VLCC hull.

the ship course, is given by

cos =

1

Wsin

U

21/2, (9)

where the plus sign is to be used for 0 < < /2, and

the minus sign for/2< < . When > /2,FW is

actually helping the ship forward. The apparent wind speed

experienced by the rotating blade element at radiusr , see

Fig.3, is given by

V = ([U(1 a)]2

+ [(1 + a

)r]2

)1/2

, (10)

wherea is the fractional decrease in wind speed when the

wind reaches the blade, a accounts for the induced rotation

of the wind field at the blade, and is the wind turbine

rotation rate in rad/s.

The power extracted from the wind by the blade element of

widthdr is given as the product of the tangential compo-

nent of the aerodynamic force acting on the blade element

times the tangential velocity component of the blade ele-

ment,r, i.e.

dP = 12

acN V2(CLsin CDcos )rdr, (11)

whereN is the number of blades, is the apparent wind

angle,c is the chord, and CL andCD are the lift and drag

c

U(1-a)

r(1+a')

V

Figure 3: Wind turbine blade element with air velocity com-

ponents.

coefficients of the blade element respectively. The forward

force produced by the water propeller can be derived from

the wind turbine power as

dF =dP/u, (12)

where is the overall efficiency factor of the driving mech-

anism, which consists of all components transmitting the


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power between the wind turbine and the water propeller as

well as the water propeller itself.

The backward force on the wind turbine will have a com-

ponent transverse to the motion of the ship as well as par-

allel to it. Assuming that the transverse force is balanced

by a lifting force due to a small leeway angle between the

ship and its path, the transverse force component can be

ignored. The longitudinal component is given as

dFW = 1

2acN V

2(CLcos + CDsin )dr cos . (13)

The net forward force,dF dFW, is found when combin-

ing Eqs. (11),(12) and(13) as

dFdFW =1

2acCLN V

2

r

u (sin cos ) (cos + sin )cos

dr,

(14)

where = CD/CLis the drag-to-lift ratio of the airfoil sec-

tion. From momentum theory, we know that the backward

force on the wind turbine can be written as

dFW = 4aU2a(1 a)rdr cos . (15)

The power,dP, can be written as

dP = dQ=

1

2 acNV2

CL(sin cos )rdr, (16)

where the torque,dQ, exerted on the blade elements by the

fluid annulus of width dr can from momentum theory be

written as

dQ= U(1 a)4ar3adr. (17)

The alternative expression for dP, dP = dQ, then be-

comes

dP =U(1 a)4a2r3adr. (18)

Combining Eqs. (12), (18), and(15), the total net forward

force can be written as

Fnet4aR2W2

=1 + f2 + 2fcos

S2

S0

a(1 a)H(s)sds,

(19)

where R is the wind turbine rotor radius, S= R/Uis the

tip speed ratio,s = r/Uis the dimensionless speed ratio

and the functionH(s)is given by

H(s) =U

u

as2

a

cos , (20)

whereU /u can be obtained from Eq.(8) and cos

fromEq. (9).

Now, let us keep , f, and fixed, set = 0, and try

to maximize Fnet with respect to a(s) and S. It can be

shown (Blackford, 1985)thata is related toathrough

a(s) = 1

2(1 + /s)

+1

2(1 + /s)2 + 4a[(1 a)/s2 /s]. (21)Blackford found that the function

a(s) a0[1 exp(2s)] (22)

gives a good approximation for the maximumFnet values.

As discussed byGlauert(1943), the maximum velocity re-

duction in the slipstream, 2U a, only occurs on the vortex

sheets formed by the trailing vortices from the blade tips.

The circumferential average decrease of axial velocity in

the slipstream is only a fraction G of this velocity. The

wind speed reduction parameter a should therefore be mul-

tiplied withG to account for a finite number of blades, N.

An approximate expression forG was first worked out by

Prandtl, known as Prandtls tip loss factor:

G= 2

arccos [exp (g)], (23)

where

g= N

2(1 s/S)

1 + S2. (24)

The optimal apparent wind angle,, can be found from

(s) = arctan1

s1 a

1 + a

, (25)

wherea and a are determined from Eq. (22)and Eq. (21)

respectively.(r)can be found by substituting s= rU into

Eq. (25).

By combining Eqs. (13)and (15), we get an expression for

the chord length:

c= 8U2a(1 a)r

N V2(CLcos + CDsin ). (26)

From Fig.3,we have

sin2 =U2(1 a)2

V2 , (27)

and by inserting this into Eq.(26), we get

c= 8r sin2()a

N(CLcos + CDsin )(1 a). (28)

This is a different expression than what Blackford obtained

for c.

3 FUEL SAVING FOR A NOTIONAL WIND TURBINE

SHIP

As a result of the considerations discussed above, in the fol-

lowing calculations, a 150 m long ship with the same hull

as studied in Fig.1is theoretically fitted with a four-bladed

39 m diameter horizontal-axis wind turbine for auxiliary


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propulsion, and set to sail the route Peterhead - Bremer-

haven - Peterhead, see Fig. 4. This route is chosen pri-

marily due to the weather stations in close proximity to the

route, for which statistical wind data is available. The route

is divided into 8 legs, where the wind data for each leg is

taken from the closest weather station. Table2 gives the

dominant wind directions and average wind speeds for the

different legs in January, 10 m above sea level. In order to

calculate the wind speeds at an elevation of 39.5 m above

sea level, which is the hub height of the notional wind tur-

bine ship, Eq. (29)is used:

U(z) = U10

z10

, (29)

where U(z) is the mean wind speed at elevation z , U10 is

the mean wind speed at 10 m elevation, and = 1/7 =

0.1429 is a typical value of (Peterson and Hennessey,

1978).

For given values of,W, f, and, there is a value ofa0,

see Eq.22, that gives the maximum possible net forward

force for a given wind turbine radius R. In order for the

wind turbine to operate at different values of a0, a different

blade design is required for each combination of,W, f,

if is fixed. This is, of course, totally impractical, and a

practical alternative is to use a wind turbine with control-

lable blade pitch. However, it is not possible to obtain the

exact optimal pitch for all radii if the blade is turned a cer-

tain angle from, say, the optimal upwind blade pitch. As

Blackford points out, it would likely be best to design thewind turbine for optimal performance upwind, since this is

the most important and most critical direction. The blades

should, nevertheless, be able to be turned in order to opti-

mize the net forward force at different wind directions and

wind speeds, and to have full control of the wind turbine

and its loads in strong winds.

From the discussion above, the optimized wind turbine ship

is designed to sail at 10 kn, with = 0 and W= 20 kn =

10.288 m/s, so f= 0.5. It is assumed that all blade sections

operate at an angle of attack of = 4, and thatCL = 0.8

andCD = 0.024. The chord and pitch angle distributions,see Table3, are hence fixed, as they are designed for opti-

mal upwind performance, but the blades can be turned, and

regulated by a gearing mechanism, to maximize Fnet for

the specific combination of, W, andf.

With the chord and pitch angle distributions known, the

wind reduction factor,a, is now calculated from Eq.(28).

Solving Eq. (28) forayields

a= b

1 + b, (30)

where

b= cN(CLcos + CDsin )

8r sin2 . (31)

Knowing a, a is then calculated from Eq. (21). We can

now check if the values ofa,a andresults in the correct

r [m] [deg] c [m]

1 70.8 1.26

3 52.3 3.58

5 40.2 4.30

7 32.1 4.18

9 26.5 3.79

11 22.5 3.34

13 19.6 2.91

15 17.5 2.46

17 16.2 1.93

19 16.0 0.97

19.5 16.9 0

Table 3: Design parameters for the four-bladed optimized

wind turbine.

, see Fig. 3. An iteration procedure must be performedfor different angles of attack, , at each radial blade posi-

tion, to find the which gives the correct . The NACA

4412 foil section is used here, with CL as a function of

given inAbbott and von Doenhoff (1959). It is assumed

thatCD =CL, where = 0.03.

By adjusting the rotation rate and blade angle, for a

given blade design, we can get relatively close to the op-

timalFnet if the blades were designed specifically for the

actual values of, W, and f. Fnet is found through nu-

merical integration of Eq. (14). The net power in Table4

is defined as the power generated by the wind turbine mi-nus the power required to overcome the backward force on

the wind turbine rotor disk, and can be calculated by mul-

tiplying the net force with the ship speed and divide by the

efficiency factor2, which accounts for losses from the en-

gine to the propeller, and propeller losses. With a generator

efficiency,1 = 0.95, the overall efficiency factor then be-

comes = 12, and is assumed to be = 0.7 here. The

total energy saved using the optimized blade design for

= 0, W = 10.288 m/s, and f = 0.5, when adjusting the

wind turbine rotation rate and blade angle, is 40630 kWh.

This equals33.1% of the total required energy, includinga sea margin of 15%. A simplified model for the drag on

the wind turbine tower is included in the calculations: The

tower is divided into two vertical cylinders, one covered by

the wind turbine and one uncovered by the wind turbine.

The drag force on the tower,FD,t , is then calculated as

FD,t =CD,t1

2a(Ucos

)2

At,uncovered

+ CD,t1

2a(U(1 a)cos

)2

At,covered , (32)

whereCD,t is the drag coefficient of the cylindrical tower,

At,uncovered andAt,covered are the projected areas of thewind turbine tower that are uncovered and covered by the

wind turbine, respectively. In the calculations, the follow-

ing estimated values are used: a = 0.1, At,uncovered = 30


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Figure 4: The route for the wind turbine ship.

m2,At,covered = 48.75 m2 andCD,t = 1.17.

In order to study the effect of optimizing the wind turbine

design for a given wind turbine diameter, similar calcula-

tions are done for a Vestas V39/600 wind turbine onboard

the ship, see Fig. 5. The Vestas V39/600 has a rotor di-

ameter of 39 m, and can generate up to 600 kW of power.

Using the power coefficient, Eq. (7), wherePis the power

found from the power curve (El-Shimy,2010)for a given

wind speed, the axial induction factor,a, is then calculated

by solving the cubic equation

4a3 8a2 + 4a CP = 0. (33)

Note that Eq. (33)has no solution ifCP is above the Betzlimit. Solutions of Eq. (33) larger than 0.4 are not valid,

due to the limitations of momentum theory. Using ax-

ial momentum theory, the component of the force on the

wind turbine in the direction of the ship course is given by

Eq. (1).

Again, the net force is calculated as the power generated

by the wind turbine minus the power required to overcome

FW at 10 knots. As we see from Table4, employing the

Vestas V39/600 wind turbine on the notional wind turbine

ship will result in a total energy saving of24.4% for the

given ship and route, compared to33.1%for the optimizedwind turbine design. The drag on the Vestas V39/600 wind

turbine tower is set equal to the drag on the optimized wind

turbine tower, and again, a sea margin of 15% is used.

Figure 5: Illustration of a Vestas V39/600 wind turbine on-

board a tanker for power generation.

4 COMPARISON WITH WINGSAILS

The fuel saving attained for the optimized notional wind

turbine ship is compared with that of a notional ship of the

same dimensions, using wingsails instead of a wind turbine

for auxiliary propulsion. The maximum possible sail area

for a particular ship, is

SA = K

D

2/3

, (34)

where D is the volume displacement of the ship, and K is

a constant, which has the value 3.2 for wingsails (Asker,

1985). Using Eq.(34), the maximum possible sail area for


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Leg Distance Closest weather station

Dominant

wind direc-

tion

Average wind

speed [m/s]

10 m above

sea level

Peterhead - a 63.01 km Peterhead Harbour SxSW 6.7

a - b 150.26 km Forties 3 Platform SxSW 9.3

b - c 144.97 km Ekofisk Platform SxSW 12.9

c -d 140.62 km Tyra Oest ExSE 12.9

d - e 118.39 km Nordseeboje 2 ExSE 9.8

e - f 91.36 km Feuerschiff Dt. Bucht N 9.8

f - g 48.15 km Leuchtturm Alte Weser SW 10.3

g - Bremerhaven 29.65 km Bremerhaven SxSW 6.2

Table 2: Route with wind data for January (Windfinder, 2010).

our ship is 3130.5 m2. In order to compare the propul-

sive force for the wingsail-equipped ship with that of the

wind turbine-powered ship, a wingsail area equal to the ro-

tor disk area of the wind turbine is chosen. With 10 half-

elliptical wingsails of maximum chord length 6.08 m and

height 25 m, the total wingsail area is 1194.1 m2, which is

approximately equal to the rotor disk area of the wind tur-

bine, and also well below the limiting maximum possible

sail area. It is assumed a 1 m gap between the wingsails

and the ship deck, and that this gap is so small that the in-

duced drag is that corresponding to an elliptical wing of

half-span equal to the wingsail height. According to Ho-

erner (1965), this assumption is justified for gaps below0.06 of the sail height. It is further assumed that the in-

coming wind is undisturbed by the ship, and that the wind

speed at half the wingsail height is representative for the

whole wingsail. The wingsail masts are assumed to be 1 m

high and 2 m in diameter, which gives a small additional

contribution to the total drag.

The wingsail masts are spaced two maximum chord lengths

apart, and it is assumed that the local wind at one wing-

sail is not affected by the other wingsails. This assump-

tion is least incorrect when the apparent wind is abeam.

When the wind direction is directly aft, experimental re-sults on groups of longitudinally spaced flat plates normal

to the flow(Ball and Cox, 1978) are used to calculate the

drag force. It should be noted that the experimental results

were obtained at a Reynolds number of3.9 103, while in

our case, the Reynolds number based on maximum chord

length is up to 6.9 106. However, as the drag coefficient

for a flat plate normal to the flow is almost constant for a

wide range of Reynolds numbers, we believe that it is jus-

tifiable to apply these experimental results also for higher

Reynolds numbers. The wingsails are assumed to be unaf-

fected by each other until the wind angle is so large thatthe wingsails begin to shield each other, not accounting

for spreading or deflection of the wake, which we consider

to be a conservative assumption. From this wind angle, a

straight line is drawn down to the drag value for normal flat

plates, as shown in Fig.6.

The wingsails are assumed to have symmetrical cross sec-

tions of NACA 0015 profiles. The lift,FL, and drag,FD,

of the wingsails are calculated as

FL=1

2aCLSU

2, (35)

FD =1

2aCDSU

2, (36)

whereS is the wingsail area, and the two-dimensional lift

and drag coefficients, cl andcd, are found fromSheldahl

and Klimas(1981) for all angles of attack. Taking the finitespan effect into account for the half-elliptical wingsails, the

three-dimensional lift and drag coefficients become

CL= cl

1 + 2Asp, (37)

CD =cd+ C2LAsp

. (38)

The total net forward force for the 10 wingsails, Fnet,totis

then found as

Fnet,tot

= 10(FL

sin FD

cos ), (39)

where the maximum values ofFnet,tot, found by varying

the angle of attack, is plotted in Fig. 6. The resulting

fuel saving for the wingsail-equipped ship sailing the same

route at 10 knots, with a 15% sea margin, is 31.8%.

In order to compare the heeling moments of the wind tur-

bine and wingsail rigs, let us look at the following scenario:

The ship is sailing at 10 knots, with true wind direction

104.9 relative to the ship, in 20 m/s true wind speed, so

that the apparent wind direction is 90. The heeling mo-

ment due to the optimized wind turbine rig about the center

of gravity of the ship is now 6.08 MNm, whereas it is only

1.24 MNm for a Vestas V39/600 onboard the ship. The the-

ory is here applied to get the maximum Fnet for the opti-

mized wind turbine, which gives both a much larger P and


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Interpolation line

Drag on group of flat plates normal to flow

Wingsails unaffected by each other

Fnet,

tot

[N]

True wind angle [deg]

0 20 40 60 80 100 120 140 160 180

104

1

0

1

2

3

4

5

Figure 6: Net forward force from wingsails for a wind speed of 6.7 m/s, 10 m above sea level.

Leg

Net power

with opti-

mized wind

turbine design

for f = 0.5,

= 0, W = 20

kn [kW]

Net power

with

Vestas

V39/600

[kW]

Net power

with

wingsails

[kW]

Time in

leg [h]

Energy saved

with opti-

mized wind

turbine design

for f = 0.5,

= 0, W = 20

kn [kWh]

Energy

saved with

Vestas

V39/600

[kWh]

Energy

saved with

wingsails

[kWh]

Peterhead - a 107 172 312 3.40 365 584 1060

a - b 325 370 554 8.11 2635 3002 4495

b - c 863 492 1018 7.83 6759 3850 7973

c - d 1195 395 60 7.59 9075 2996 457

d - e 497 343 34 6.39 3179 2191 216e - f 295 368 417 4.93 1455 1818 2058

f - g 613 355 132 2.60 1594 923 343

g - Bremerhaven 81 134 272 1.60 129 215 435

Bremerhaven - g 69 110 245 1.60 110 175 392

g - f 240 292 397 2.60 624 759 1033

f - e 426 375 573 4.93 2099 1850 2829

e - d 167 215 241 6.39 1068 1375 1543

d - c 560 644 537 7.59 4256 4893 4079

c - b 867 539 958 7.83 6784 4218 7499

b - a 300 362 510 8.11 2435 2941 4139

a - Peterhead 95 144 282 3.40 324 491 959Sum 84.93 40630 30019 39023

Table 4: Energy savings for the ship.


9/10

Rightingmoment[MNm]

Heel angle, [deg]0 5 10 15

0

40

80

120

160

200

Figure 7: Righting moment for the ship studied.

thrust on the rotor than we get from the Vestas V39/600.

This can be seen from the power coefficient, CP, for the op-

timized wind turbine, which is 0.3144, whereas the power

coefficient for the Vestas V39/600 is only 0.0606 at this

wind speed, resulting in a power output of 600 kW. The

optimized wind turbine gives a higher net forward thrust

than the Vestas V39/600, not because the thrust is lower,

but because the power is much higher. This result may

seem somewhat counterintuitive since the optimized wind

turbine is optimized for maximumFnet and not maximum

power, but is due to the fact that the optimized wind turbine

is designed for higher apparent wind speeds than the Vestas

V39/600.

For the same wind condition, the heeling moment of the

wingsail rig about the center of gravity of the ship is 4.20

MNm, for a 13.8 angle of attack. An extreme heeling mo-

ment may occur if the wingsail rig is positioned to sail up-

wind, and the wind direction suddenly changes to 20 m/s

apparent beam wind, faster the wingsails are turned, so that

the angle of attack is 90. In this case, the heeling moment

will be as high as 116 MNm; fortunately only for a short

period of time if the wingsail positioning system is work-

ing properly. Such large heeling moments will never occur

for a wind turbine-powered ship.

The righting moment can be calculated as

Mrighting=wgGMsin , (40)

where wis the mass density of water, = 30600 m3 is the

volume displacement, GM = 2.63 m is the distance from the

center of gravity to the metacenter, and is the heel angle

of the ship. This GM-value accounts for the underwater

hull of the ship only. When the righting moment equals

the heeling moment, the ship will have a steady heel angle

. The righing moment curve is shown in Fig.7. We see

that for heeling moments below 10 MNm, the heel angle is

negligible.

5 CONCLUSION

The 150 m long tanker sailing the route Peterhead - Bre-

merhaven - Peterhead in January at 10 knots will save

24.4% of the total fuel by employing the Vestas V39/600

for auxiliary power generation. By optimizing the wind

turbine design for ship propulsion while keeping the wind

turbine diameter fixed at 39 m, the fuel saving increases to

33.1%. Fitting the ship with wingsails of the same sail area

as the wind turbine rotor disk area results in a fuel saving

of 31.8% at a ship speed of 10 knots. It is seen that the

heeling moment in 20 m/s apparent beam wind is lower for

a ship powerered by a Vestas V39/600 wind turbine than a

wingsail-powered ship, but higher if the ship is powered by

the optimized wind turbine described in this paper. How-

ever, if one considers the risk of the wingsail turning system

failing, a wind turbine-powered ship is preferable with re-

spect to heeling moments. For a ship sailing about half the

wind speed, it is thus seen that an optimized wind turbine-

powered ship is weakly preferable over a wingsail-poweredship, if energy efficiency and heeling moments are the main

concerns.

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